US5410498A - Decimation circuit and method for filtering quantized signals while providing a substantially uniform magnitude and a substantially linear phase response - Google Patents

Decimation circuit and method for filtering quantized signals while providing a substantially uniform magnitude and a substantially linear phase response Download PDF

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US5410498A
US5410498A US08/223,196 US22319694A US5410498A US 5410498 A US5410498 A US 5410498A US 22319694 A US22319694 A US 22319694A US 5410498 A US5410498 A US 5410498A
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magnitude
output signal
decimation
circuit
digital
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Daniel A. Staver
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General Electric Co
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General Electric Co
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Priority to TW084100037A priority patent/TW255996B/zh
Priority to ES09500540A priority patent/ES2110354B1/es
Priority to DE19510655A priority patent/DE19510655B4/de
Priority to KR1019950007810A priority patent/KR100360631B1/ko
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0283—Filters characterised by the filter structure
    • H03H17/0286—Combinations of filter structures
    • H03H17/0288—Recursive, non-recursive, ladder, lattice structures
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/04—Recursive filters
    • H03H17/0416—Recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing
    • H03H17/0427—Recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies
    • H03H17/0438—Recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies the ratio being integer
    • H03H17/045—Recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies the ratio being integer where the output-delivery frequency is lower than the input sampling frequency, i.e. decimation

Definitions

  • the present invention is generally related to decimation circuits used, for example, in oversampled delta-sigma analog-to-digital converters, and, in particular, to a decimation circuit and method for filtering quantized electrical signals while providing a substantially uniform magnitude and a substantially linear phase response at least over a desired passband range.
  • While data acquisition systems for generating digital data for the purposes of computation may receive analog input signals from a plurality of sensors, the analog signals must be digitized or quantized before they can be used by a computer as a basis for supporting computations. It is desirable to include respective analog-to-digital converters within the confines of an inexpensive single monolithic integrated circuit.
  • Such data acquisition circuitry can be constructed using metal-oxide-semiconductor (MOS) integrated circuit technology and is suited for applications such as power metering and internal-combustion engine control.
  • MOS metal-oxide-semiconductor
  • Oversampling analog-to-digital converters of delta-sigma type are particularly economical of digital hardware.
  • the use of such converter introduces the need for sinc k decimation filters, in which the kernel is a sampled-data representation of a suitable time-domain response, to achieve sufficient selectivity against harmonic components of the sinusoid being filtered.
  • the time domain response corresponds to a rectangular time response
  • the time domain response corresponds to a triangular time response.
  • the magnitude response of such sinc k filters generally introduces considerable attenuation over the high-end of a desired passband range.
  • magnitude correctors have been suggested, in general such suggested magnitude correctors typically exhibit an undesirable nonlinear phase response over the bandpass range of interest.
  • L. B. Jackson "Digital Filters and Signal Processing", 1986, available from Kluwer Academic Publishers, discusses in pages 76 and 77 various magnitude correctors, however, no suggestion is made of how to advantageously provide both a substantially uniform magnitude and a substantially linear phase response over the desired bandpass range.
  • a magnitude corrector capable of operating in a manner consistent with providing a substantially linear phase response over the passband range of interest.
  • the present invention fulfills the foregoing needs by providing a decimation circuit for filtering a stream of quantized electrical signals while providing a substantially uniform magnitude and a substantially linear phase response over a predetermined passband range F B .
  • the stream of quantized electrical signals arrives at a predetermined rate F M from an oversampling delta-sigma modulator.
  • the decimation circuit comprises a decimation filter for filtering the stream of quantized electrical signals to provide a filtered output signal at an output rate F S .
  • the decimation filter has a frequency response H( ⁇ ) defined by: ##EQU2##
  • a magnitude corrector is coupled to the decimation filter to receive the filtered output signal and to correct the magnitude of the received filtered signal at least over the predetermined range F B .
  • the decimation ratio is selected such that output rate F' S is sufficiently situated above bandpass range F B such that the magnitude corrector provides a desired substantially uniform magnitude and a substantially linear phase response over the passband range F B .
  • FIG. 1 is a block diagram showing a delta-sigma analog-to-digital converter which can conveniently incorporate a decimation circuit in accordance with the present invention
  • FIGS. 2a, 2b, and 2d illustrate exemplary power spectra associated with operations of the analog-to-digital converter of FIG. 1, while FIG. 2c and 2e represent typical filter characteristics for the decimation filter of FIG. 1;
  • FIG. 3 is a block diagram of a decimation circuit with a magnitude corrector, in accordance with the present invention.
  • FIG. 4 illustrates the z domain transfer function for the magnitude corrector of FIG. 3
  • FIG. 5 is a block diagram showing an implementation for the magnitude corrector of FIG. 4.
  • FIGS. 6a, 6b, and 6c illustrate exemplary z domain representations associated with operations of a magnitude corrector having the z domain transfer function in accordance with the present invention.
  • FIGS. 7a and 7b respectively, illustrate magnitude and phase error in a nonoversampled environment
  • FIGS. 7c and 7d respectively, illustrate magnitude and phase errors in an oversampled environment in accordance with the present invention.
  • A/D converters oversampled analog-to-digital (A/D) converters.
  • A/D converters One example of such A/D converter is delta-sigma converter 100 illustrated in FIG. 1.
  • Systems in which analog-to-digital converters and delta-sigma converters may prove useful are described in U.S. Pat. No. 5,181,033 entitled “Digital Filter for Filtering and Decimating Delta Sigma Modulator Output Signals," by Yassa et al., issued Jan. 19, 1993, U.S. Pat. No. 5,126,961, entitled “Plural-Channel Decimator Filter, as for Delta-sigma Analog-to-Digital Converters," by Carverick, issued Jun. 30, 1992, U.S. Pat. No.
  • delta-sigma analog-to-digital (A/D) converter 100 comprises an oversampled interpolative delta-sigma modulator 10 which is coupled to a low pass decimation filter 12.
  • the role of modulator 10 is to spectrally shape the quantization noise of a low resolution analog-to-digital converter so that the quantization noise is predominantly concentrated at high frequency.
  • the analog input signal x(t) to modulator 10 may comprise a main sinusoid situated in a relatively low frequency region (e.g., at about 60 Hz) and harmonics present over a bandpass frequency range having an upper bound F B (e.g., at about 1500 Hz).
  • bandpass frequency range F B Since the lower bound of such frequency range is near direct current (DC), such frequency range is conveniently referred hereinafter as bandpass frequency range F B .
  • the main sinusoid and harmonics are sampled by modulator 10 at a relatively high sample rate F M (e.g., about 1.966 MHz).
  • F M sample rate
  • Subsequent low pass filtering and decimation can be used to remove the bulk of the quantization noise, resulting in a high resolution digital output signal at a reduced conversion rate F M /R where R is the decimation ratio, or ratio of the output clock rate F' S to the input clock or sample rate F M .
  • F' S is about 3.8 KHz which is sufficient to meet the Nyquist rate sampling requirements over bandpass frequency range F B , that is, F' S is at least twice the highest spectral component expected over frequency range F B .
  • FIG. 1 the following functions are represented: input signal x(t), modulator output signal u(n) and filter output signal y(n) which constitutes the A/D converter output signal, along with the filter impulse response characteristics h(n).
  • the corresponding frequency spectra X(f), U(f) and Y(f), and filter characteristics H(f), respectively are shown in FIGS. 2a, 2b, 2d and 2c and represent the conditions in the circuit of FIG. 1 at locations (a), (b), (d) and (c) respectively.
  • a decimation filter which provides adequate attenuation for typical delta-sigma modulators comprises a frequency response given by: ##EQU3##
  • FIG. 2e shows in more detail that decimation filter 12 introduces significant magnitude attenuation or droop over bandpass range F B .
  • the dotted line represents an exemplary magnitude response for a sinc 2 decimation filter having, for example, a decimation ratio R of 512 which as previously described satisfies the Nyquist rate sampling requirements over bandpass frequency range F B .
  • the designation sinc k is conveniently used to abbreviate the mathematical relationship defined by Eq. 1.
  • the solid line represents a typical magnitude response for a sinc 2 decimation filter having, for example, a decimation ratio R of 128.
  • F' S is about 15.36 KHz so as to provide an oversampling factor of at least four relative to the lowest sampling rate required to satisfy the Nyquist rate sampling requirements over bandpass frequency range F B .
  • oversampling reduces the level of droop over the upper end of bandpass region F B , the level of droop can still detrimentally affect the accuracy of signal measurements over the bandpass region.
  • FIG. 3 shows that in accordance with an embodiment of the present invention, a magnitude corrector 20 is coupled to receive the output signal y(n) of decimation filter 12 so as to provide a magnitude corrected output signal y'(n).
  • An important requirement, for magnitude corrector 20 is to provide a substantially linear phase response over the bandpass region F B .
  • magnitude corrector 20, to reduce size and power requirements, should preferably be implemented with a minimum number of components. For example, a magnitude corrector not fulfilling the foregoing requirements would be difficult to incorporate in a single monolithic electronic integrated circuit chip for a delta-sigma converter.
  • IIR infinite impulse response
  • FIG. 5 shows that magnitude corrector 20 can be advantageously constructed with relatively few components and thus another advantage of the present invention is its simplicity of implementation.
  • a digital subtractor 25 receives the filtered output signal y(n) as a minuend input signal and receives a feedback signal as a subtrahend input signal so as to produce a difference output signal.
  • a delay unit 30 receives the difference signal to produce a delayed difference output signal which is in turn received by a digital multiplier 35 having a multiplication factor substantially corresponding to the number ⁇ .
  • the output signal of the multiplier constitutes the subtrahend input signal and the difference output signal constitutes the output of the magnitude corrector.
  • digital multiplier 35 is a multibit floating point multiplier and digital subtractor 25 is a multibit floating point subtractor.
  • the value for the number ⁇ is suitably selected depending on the particular implementation for a given decimation filter/magnitude corrector implementation.
  • FIGS. 6a-6c illustrate a z plane representation which shows the advantageous results obtained in an oversampled environment in accordance with the present invention.
  • FIG. 6a illustrates a nonoversampled environment wherein quantization data is acquired at a suitable sample rate F S so that the useful bandwidth is represented by the arc between the DC point and the half bandwidth point F S /2.
  • FIG. 6b illustrates an oversampled environment wherein quantization data is acquired at a suitable rate F' S and generally corresponding to a multiple of sample rate F S .
  • the useful bandwidth is represented by the arc between the DC point and the point corresponding to the half bandwidth F' S /2.
  • an oversampling factor of four is depicted.
  • the magnitude corrector introduces a pole located at - ⁇ and a zero located at the intersection of axes Im(z) and Re(z). It can be shown that the effect of the pole, for the oversampled case, is significantly less as compared to the non-oversampled case illustrated in FIG. 6a. Since such oversampling is directly related to decimation ratio R, a key advantage of the present invention is provided by selecting the decimation ratio such that output rate F' S is sufficiently situated above bandpass range F B to provide a desired substantially uniform magnitude and a substantially linear response over the predetermined passband range F B . Thus, when operated in such oversampled environment, the magnitude corrector having the z domain response as described in the context of FIG.
  • FIGS. 7a-7d show that the decimation circuit in accordance with the present invention, when operated in an oversampled environment, is capable of providing substantial magnitude correction and substantial linear phase response over the bandpass frequency F B .
  • FIGS. 7a and 7c shows that the magnitude error for the decimation circuit is reduced by at least a factor of 500 when the decimation circuit is used in an oversampled environment.
  • FIGS. 7b and 7d shows that the non-linearity phase error is improved by at least a factor of 100 when the decimation circuit is used in an oversampled environment.
  • decimation filter 12 (FIG. 3) has an exemplary transfer function corresponding to a sinc 2 decimation filter.
  • a method of operating a decimation circuit in accordance with the present invention may include the steps of decimation filtering the stream of quantized electrical signals to provide a filtered output signal at an output rate F' S using a decimation filter having a frequency response defined by Eq. 1; selecting the decimation ratio such that output rate F' S is sufficiently situated above bandpass range F B so as to provide a desired substantially uniform magnitude and a substantially linear phase response over the passband range F B ; and correcting the magnitude of the filtered output signal at least over the passband range F B .

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Mathematical Physics (AREA)
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US08/223,196 1994-04-05 1994-04-05 Decimation circuit and method for filtering quantized signals while providing a substantially uniform magnitude and a substantially linear phase response Expired - Lifetime US5410498A (en)

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Application Number Priority Date Filing Date Title
US08/223,196 US5410498A (en) 1994-04-05 1994-04-05 Decimation circuit and method for filtering quantized signals while providing a substantially uniform magnitude and a substantially linear phase response
TW084100037A TW255996B (en) 1994-04-05 1995-01-05 Decimation circuit and method for filtering quantized signals while providing a substantially uniform magnitude and a substantially linear phase response
ES09500540A ES2110354B1 (es) 1994-04-05 1995-03-16 Circuito de diezmado y procedimiento para el filtraje de señales cuantificadas, proporcionando al mismo tiempo una magnitud substancialmente uniforme y una respuesta de fase substancialmente lineal.
DE19510655A DE19510655B4 (de) 1994-04-05 1995-03-23 Schaltungsanordnung zum Filtern eines Stroms quantisierter elektrischer Signale und Verfahren zum Filtern eines Stoms quantisierter elektrischer Signale
KR1019950007810A KR100360631B1 (ko) 1994-04-05 1995-04-04 실질적으로균일한크기응답및실질적으로선형인위상응답의제공및양자화신호들의필터링을위한데시메이션회로및방법

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Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5650951A (en) * 1995-06-02 1997-07-22 General Electric Compay Programmable data acquisition system with a microprocessor for correcting magnitude and phase of quantized signals while providing a substantially linear phase response
US6041339A (en) * 1998-03-27 2000-03-21 Ess Technology, Inc. Efficient decimation filtering
US6393070B1 (en) * 1997-08-12 2002-05-21 Koninklijke Philips Electronics N.V. Digital communication device and a mixer
US6470365B1 (en) * 1999-08-23 2002-10-22 Motorola, Inc. Method and architecture for complex datapath decimation and channel filtering
US6816100B1 (en) 1999-03-12 2004-11-09 The Regents Of The University Of California Analog-to-digital converters with common-mode rejection dynamic element matching, including as used in delta-sigma modulators
US8036419B2 (en) 1998-04-16 2011-10-11 Digimarc Corporation Digital watermarks
US10862505B1 (en) 2020-02-27 2020-12-08 Nxp Usa, Inc. Arbitrary rate decimator and timing error corrector for an FSK receiver

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KR100799406B1 (ko) 2004-06-22 2008-01-30 삼성탈레스 주식회사 대역 내 신호의 감쇠를 보상하기 위한 디지털 샘플링레이트 변환기
KR101949580B1 (ko) * 2017-03-02 2019-02-18 서울대학교산학협력단 주파수 특성을 보정하는 아날로그 디지털 변환기 및 이를 포함하는 반도체 장치

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Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5650951A (en) * 1995-06-02 1997-07-22 General Electric Compay Programmable data acquisition system with a microprocessor for correcting magnitude and phase of quantized signals while providing a substantially linear phase response
US6393070B1 (en) * 1997-08-12 2002-05-21 Koninklijke Philips Electronics N.V. Digital communication device and a mixer
US6041339A (en) * 1998-03-27 2000-03-21 Ess Technology, Inc. Efficient decimation filtering
US8036419B2 (en) 1998-04-16 2011-10-11 Digimarc Corporation Digital watermarks
US6816100B1 (en) 1999-03-12 2004-11-09 The Regents Of The University Of California Analog-to-digital converters with common-mode rejection dynamic element matching, including as used in delta-sigma modulators
US6470365B1 (en) * 1999-08-23 2002-10-22 Motorola, Inc. Method and architecture for complex datapath decimation and channel filtering
US10862505B1 (en) 2020-02-27 2020-12-08 Nxp Usa, Inc. Arbitrary rate decimator and timing error corrector for an FSK receiver

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KR100360631B1 (ko) 2003-01-24
ES2110354A1 (es) 1998-02-01
ES2110354B1 (es) 1998-08-01
KR950035063A (ko) 1995-12-30
TW255996B (en) 1995-09-01
DE19510655B4 (de) 2006-04-27
DE19510655A1 (de) 1995-10-12

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